Properties

Genus \(3\)
Quotient Genus \(0\)
Group \(S_3\)
Signature \([ 0; 2, 2, 2, 2, 3 ]\)
Generating Vectors \(9\)

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Family Information

Genus: 3
Quotient Genus: 0
Group name: $S_3$
Group identifier: [6,1]
Signature: $[ 0; 2, 2, 2, 2, 3 ]$
Conjugacy classes for this refined passport: 2, 2, 2, 2, 3

Jacobian variety group algebra decomposition:$E\times E^{2}$
Corresponding character(s): 2, 3

Other Data

Hyperelliptic curve(s):No
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $a_1(x^4 +y^4 +z^4)+a_2 (x^2y^2 +x^2z^2 +y^2z^2)+ a_3 (x^2yz +y^2xz +z^2xy) = 0$

Generating Vector(s)

Displaying 9 of 9 generating vectors for this refined passport.

3.6-1.0.2-2-2-2-3.1.1

  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)
  (1,6) (2,5) (3,4)
  (1,2,3) (4,5,6)

3.6-1.0.2-2-2-2-3.1.2
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)
  (1,6) (2,5) (3,4)
  (1,4) (2,6) (3,5)
  (1,3,2) (4,6,5)

3.6-1.0.2-2-2-2-3.1.3
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)
  (1,6) (2,5) (3,4)
  (1,5) (2,4) (3,6)
  (1,2,3) (4,5,6)

3.6-1.0.2-2-2-2-3.1.4
  (1,4) (2,6) (3,5)
  (1,6) (2,5) (3,4)
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)
  (1,2,3) (4,5,6)

3.6-1.0.2-2-2-2-3.1.5
  (1,4) (2,6) (3,5)
  (1,6) (2,5) (3,4)
  (1,4) (2,6) (3,5)
  (1,6) (2,5) (3,4)
  (1,3,2) (4,6,5)

3.6-1.0.2-2-2-2-3.1.6
  (1,4) (2,6) (3,5)
  (1,6) (2,5) (3,4)
  (1,6) (2,5) (3,4)
  (1,6) (2,5) (3,4)
  (1,2,3) (4,5,6)

3.6-1.0.2-2-2-2-3.1.7
  (1,4) (2,6) (3,5)
  (1,6) (2,5) (3,4)
  (1,6) (2,5) (3,4)
  (1,5) (2,4) (3,6)
  (1,3,2) (4,6,5)

3.6-1.0.2-2-2-2-3.1.8
  (1,4) (2,6) (3,5)
  (1,6) (2,5) (3,4)
  (1,5) (2,4) (3,6)
  (1,4) (2,6) (3,5)
  (1,3,2) (4,6,5)

3.6-1.0.2-2-2-2-3.1.9
  (1,4) (2,6) (3,5)
  (1,6) (2,5) (3,4)
  (1,5) (2,4) (3,6)
  (1,5) (2,4) (3,6)
  (1,2,3) (4,5,6)

Display number of generating vectors: